JEE Math Practice Question

The function $$f(x) = \left\{ {\begin{matrix} {{\pi \over 4} + {{\tan }^{ - 1}}x,} & {\left| x \right| \le 1} \\ {{1 \over 2}\left( {\left| x \right| - 1} \right),} & {\left| x \right| > 1} \\ \end{matrix} } \right.$$ is :

1. A.continuous on R–{–1} and differentiable on R–{–1, 1}
2. B.both continuous and differentiable on R–{1}
3. C.both continuous and differentiable on R–{–1}
4. D.continuous on R–{1} and differentiable on R–{–1, 1}